1. Name:__________ warm-up 6-2 Using f(x) = 3x + 2 and g(x) = 2x 2 – 1, find (f – g)(x), if it exists. Using f(x) = 3x + 2 and g(x) = 2x 2 – 1, find (f ● g)(x), if it exists. Using f(x) = 3x + 2 and g(x) = 2x 2 – 1, find [f ○ g](x), if it exists. Using f(x) = 3x + 2 and g(x) = 2x 2 – 1, find [g ○ f](x), if it exists.

2. To obtain a retail price, a dress shop adds $20 to the wholesale cost x of every dress. When the shop has a sale, every dress is sold for 75% of the retail price. If f(x) = x + 20 and g(x) = 0.75x, find [g ○ f](x) to describe this situation. Let f(x) = x – 3 and g(x) = x 2. Which of the following is equivalent to (f ○ g)(1) A.f(1) B.g(1) C.(g ○ f)(1) D.f(0)

3. Details of the Day EQ: How do radical functions model real-world problems and their solutions? How are expressions involving radicals and exponents related? I will be able to… Find the inverse of a function or relation. Determine whether two functions or relations are inverses. Activities: Warm-up Review homework Review more questions from the MP Exam Notes: Inverse Functions and Relations Class work/ HW Vocabulary:. inverse relation inverse function

4. Inverse Functions and Relations The inverse of a function has all the same points as the original function, except that the x 's and y 's have been reversed.

5. A Quick Review Using f(x) = 3x + 2 and g(x) = 2x 2 – 1, find (f – g)(x), if it exists. Using f(x) = 3x + 2 and g(x) = 2x 2 – 1, find (f ● g)(x), if it exists. Using f(x) = 3x + 2 and g(x) = 2x 2 – 1, find [f ○ g](x), if it exists. Using f(x) = 3x + 2 and g(x) = 2x 2 – 1, find [g ○ f](x), if it exists.

6. A Quick Review To obtain a retail price, a dress shop adds $20 to the wholesale cost x of every dress. When the shop has a sale, every dress is sold for 75% of the retail price. If f(x) = x + 20 and g(x) = 0.75x, find [g ○ f](x) to describe this situation.

7. A Quick Review Let f(x) = x – 3 and g(x) = x 2. Which of the following is equivalent to (f ○ g)(1) A.f(1) B.g(1) C.(g ○ f)(1) D.f(0)

8. Notes and examples GEOMETRY The ordered pairs of the relation {(1, 3), (6, 3), (6, 0), (1, 0)} are the coordinates of the vertices of a rectangle. Find the inverse of this relation. Describe the graph of the inverse.

9. Notes and examples GEOMETRY The ordered pairs of the relation {(–3, 4), (–1, 5), (2, 3), (1, 1), (–2, 1)} are the coordinates of the vertices of a pentagon. What is the inverse of this relation?

10. Notes and examples GEOMETRY The ordered pairs of the relation {(–3, 4), (–1, 5), (2, 3), (1, 1), (–2, 1)} are the coordinates of the vertices of a pentagon. What is the inverse of this relation?

11. Notes and examples Then graph the function and its inverse. Step 4Replace y with f –1 (x). Step 3 Solve for y. Step 1Replace f(x) with y in the original equation Step 2Interchange x and y.

12. Notes and examples Graph the function and its inverse.

13. Notes and examples

14. A.They are not inverses since [f ○ g](x) = x + 1. B.They are not inverses since both compositions equal x. C.They are inverses since both compositions equal x. D.They are inverses since both compositions equal x + 1.